Quantiles are cutpoints dividing a set of observations into equal sized groups. There are one fewer quantiles than the number of groups created. Thus quartiles are the 3 cut points that will divide a dataset into four equal-size groups. Common quantiles have special names: for instance quartile, decile (creating 10 groups: see below for more). The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points.
q-Quantiles are values that partition a finite set of values into q subsets of (nearly) equal sizes. There are q − 1 of the q-quantiles, one for each integer k satisfying 0 < k < q. In some cases the value of a quantile may not be uniquely determined, as can be the case for the median (2-quantile) of a uniform probability distribution on a set of even size. Quantiles can also be applied to continuous distributions, providing a way to generalize rank statistics to continuous variables. When the cumulative distribution function of a random variable is known, the q-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values {1/q, 2/q, …, (q − 1)/q}.
Scribere proposui de contemptu mundano
ut degentes seculi non mulcentur in vano
iam est hora surgere
a sompno mortis pravo
a sompno mortis pravo
Vita brevis breviter in brevi finietur
mors venit velociter quae neminem veretur
omnia mors perimit
et nulli miseretur
et nulli miseretur.
Ad mortem festinamus
peccare desistamus
peccare desistamus.
Ni conversus fueris et sicut puer factus
et vitam mutaveris in meliores actus
intrare non poteris
regnum Dei beatus
regnum Dei beatus.
Tuba cum sonuerit dies crit extrema
et iudex advenerit vocabit sempiterna
electos in patria
prescitos ad inferna
prescitos ad inferna.